Icarus 221 (2012) 365–387 Contents lists available at SciVerse ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Absolute magnitudes of asteroids and a revision of asteroid albedo estimates from WISE thermal observations ⇑ Petr Pravec a, , Alan W. Harris b, Peter Kušnirák a, Adrián Galád a,c, Kamil Hornoch a a Astronomical Institute, Academy of Sciences of the Czech Republic, Fricˇova 1, CZ-25165 Ondrˇejov, Czech Republic b 4603 Orange Knoll Avenue, La Cañada, CA 91011, USA c Modra Observatory, Department of Astronomy, Physics of the Earth, and Meteorology, FMFI UK, Bratislava SK-84248, Slovakia article info abstract Article history: We obtained estimates of the Johnson V absolute magnitudes (H) and slope parameters (G) for 583 main- Received 27 February 2012 belt and near-Earth asteroids observed at Ondrˇejov and Table Mountain Observatory from 1978 to 2011. Revised 27 July 2012 Uncertainties of the absolute magnitudes in our sample are <0.21 mag, with a median value of 0.10 mag. Accepted 28 July 2012 We compared the H data with absolute magnitude values given in the MPCORB, Pisa AstDyS and JPL Hori- Available online 13 August 2012 zons orbit catalogs. We found that while the catalog absolute magnitudes for large asteroids are relatively good on average, showing only little biases smaller than 0.1 mag, there is a systematic offset of the cat- Keywords: alog values for smaller asteroids that becomes prominent in a range of H greater than 10 and is partic- Asteroids ularly big above H 12. The mean (H H) value is negative, i.e., the catalog H values are Photometry catalog À Infrared observations systematically too bright. This systematic negative offset of the catalog values reaches a maximum around H = 14 where the mean (Hcatalog À H)isÀ0.4 to À0.5. We found also smaller correlations of the offset of the catalog H values with taxonomic types and with lightcurve amplitude, up to 0.1 mag or less. We discuss a few possible observational causes for the observed correlations, but the reason for the large bias of the catalog absolute magnitudes peaking around H = 14 is unknown; we suspect that the problem lies in the magnitude estimates reported by asteroid surveys. With our photometric H and G data, we revised the preliminary WISE albedo estimates made by Masiero et al. (Masired, J.R. et al. [2011]. Astrophys. J. 741, 68–89) and Mainzer et al. (Mainzer, A. et al. [2011b]. Astrophys. J. 743, 156–172) for asteroids in our sample. We found that the mean geometric albedo of Tholen/Bus/DeMeo C/G/B/F/P/D types with sizes of 25–300 km is pV = 0.057 with the standard deviation (dispersion) of the sample of 0.013 and the mean albedo of S/A/L types with sizes 0.6–200 km is 0.197 with the standard deviation of the sample of 0.051. The standard errors of the mean albedos are 0.002 and 0.006, respec- tively; systematic observational or modeling errors can predominate over the quoted formal errors. There is apparent only a small, marginally significant difference of 0.031 ± 0.011 between the mean albedos of sub-samples of large and small (divided at diameter 25 km) S/A/L asteroids, with the smaller ones having a higher albedo. The difference will have to be confirmed and explained; we speculate that it may be either a real size dependence of surface properties of S type asteroids or a small size-dependent bias in the data (e.g., a bias towards higher albedos in the optically-selected sample of asteroids). A trend of the mean of the preliminary WISE albedo estimates increasing with asteroid size decreasing from D 30 down to 5 km (for S types) showed in Mainzer et al. (Mainzer, A. et al. [2011a]. Astrophys. J. 741, 90–114) appears to be mainly due to the systematic bias in the MPCORB absolute magnitudes that progressively increases with H in the corresponding range H = 10–14. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction with adaptive optics systems or radar observations, and asteroid occultations of stars. However, use of the direct techniques is lim- Diameters and albedos of asteroids are one of their most basic ited mostly to large asteroids or those making close approaches to physical parameters. Asteroid diameters can be estimated with the Earth. Indirect techniques of asteroid size estimation are polar- several direct or indirect techniques. Direct size estimation tech- imetry, from which one determines albedo and with an absolute niques include in situ spacecraft observations, resolved imaging magnitude value can compute a diameter, and asteroid thermal modeling with observations of their thermal infrared and visual fluxes; the effective diameter and visual geometric albedo are ⇑ Corresponding author. Fax: +420 323 620263. parameters of asteroid thermal models. This latter technique has E-mail address: [email protected] (P. Pravec). 0019-1035/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2012.07.026 366 P. Pravec et al. / Icarus 221 (2012) 365–387 been applied to large samples of asteroids covering a broad range asteroids in our sample were targeted observations—the asteroids of sizes. were selected and observed deliberately for particular aims of the Ideally, both the integral thermally emitted infrared and the specific photometric projects. A fraction (96 of the 583) were, how- integral reflected optical fluxes should be measured simulta- ever, accidental observations of asteroids that happened to be neously. In practice, however, thermal observations are normally present in the imaged fields of the targeted asteroids. Our target made at a single or over a limited range of aspects, and it has be- selection procedures favored certain types of heliocentric orbits, come a normal practice for asteroid thermal modellers to estimate namely near-Earth and inner main-belt (including Hungarias), the integral optical flux from the asteroid’s absolute visual magni- but they were blind to other asteroid parameters such as visible tude H and a model of its phase function.1 The absolute magnitude color or discovery stations/circumstances. The accidentally ob- of a Solar System object is defined as the apparent magnitude of the served asteroids were not selected even for heliocentric orbits of object illuminated by the solar light flux at 1 AU and observed from a course; more than a half of them were central and outer main-belt distance of 1 AU and at zero solar phase angle (the angle between asteroids. We outline our observational and reduction procedures the asteroid–observer and the asteroid–Sun lines). in the following paragraphs. Absolute magnitudes of asteroids are estimated from their pho- tometric observations. As the observations are generally taken at 2.1. Absolute calibrations in the Johnson–Cousins BVRI system non-zero solar phase angles, an estimation of H involves an estima- tion of the dependence of the asteroid brightness on the phase an- We made the observations primarily through the V or R filters gle. The dependence is most often modeled with the H–G phase and calibrated them in the Johnson–Cousins system using the relation (Bowell et al., 1989) that has conveniently only two free Landolt standard stars (Landolt, 1973, 1983, 1992) with the all- parameters, the absolute magnitude H and the slope parameter sky photometry method on photometric nights. We observed some G. The systematic model error of the H–G phase relation is on an of the asteroids also in other than just the primary filter and in order of a few 0.01 mag (Harris, 1989). such cases we estimated their actual color indices. However, many Thermal infrared survey observations by the Infrared Astronom- of the asteroids were observed in only the primary filter, R in the ical Satellite (IRAS), the Wide-field Infrared Survey Explorer (WISE), case of the Ondrˇejov observations, as with CCD cameras we AKARI and the Spitzer Space Telescope resulted in estimates of achieved a higher signal-to-noise ratio and a lower atmospheric diameters and albedos for thousands of asteroids (e.g., Tedesco extinction compared to the V band. The spectral transmission et al., 2002; Mainzer et al., 2011a,b; Masiero et al., 2011; Usui curve of the R filter was designed for a given CCD so that the result- et al., 2011; Ryan and Woodward, 2011). They used the absolute ing spectral response of the telescope + filter + CCD combination magnitude values from the asteroid orbit catalogs MPCORB2 or matched closely the Cousins R passband as defined in Bessell AstOrb.3 Most of the absolute magnitudes in the catalogs were de- (1990); the coefficient of the color term, in which we use (V À I), rived from magnitude estimates reported by visual asteroid surveys in the photometric transformation function of the telescope system and follow-up observers with their astrometric observations. The was always within 0.05 of zero. With such a filter + CCD setup, we procedures that most of the astrometric surveys, follow-up observ- were able to calibrate the asteroid photometric observations in the ers, and orbit calculators used for estimating the asteroid apparent Cousins R system assuming (V À I) of 0.80, which is about the aver- magnitudes and derivation of the H values have not been compre- age asteroidal color index, with a systematic error <0.01 mag; the hensively published so far. most common C and S asteroid types have a mean (V À I) of 0.73 Given the principal importance of asteroid absolute magnitude and 0.90, respectively (Shevchenko and Lupishko, 1998). With data for the estimation of their diameters and albedos and consid- the use of several Landolt standard stars for the calibrations on ering that the accuracy of and biases present in the H values in the each photometric night, we defined the magnitude system’s zero orbit catalogs have not been satisfactorily characterized so far,4 we point with accuracy of 0.01 mag.